Board game based on four-color theorem

Abstract

To prove a four-color theorem, and to provide a board game that allows one to enjoy the game by thinking and competing using a uniform rule utilizing the means and a rule of the four-color theorem.SOLUTION: In a board game based on a four-color theorem comprising multiple board surfaces having a map consisting of multiple grids and multiple pieces having four knobs having different colors disposed based on a rule of a four-color theorem, teams are divided into an attacking side team and a defensing side team, and they compete each other for the total number of pieces placed on the board surfaces.SELECTED DRAWING: Figure 16

Description

Technical Field

[0001] The present invention relates to a toy in which a plurality of pieces are arranged according to the rule of the four-color theorem on a board on which a map with a grid is drawn.

Background Art

[0002] Although there have been many board games so far, while the proof of the four-color theorem, which is said to be a difficult problem in mathematics, has not been done without using a computer, by simultaneously disclosing this proof in the present application, an original board game that plays according to the rule of the four-color theorem is provided.

Disclosure of the Invention

Problems to be Solved by the Invention

[0003] Since the four-color theorem requires that all regions of the entire map can be colored with four colors, the means itself has been a problem. However, although the problem and the coloring are not difficult and a complete answer cannot be given, the process was felt to be as enjoyable as solving a quiz.

[0004] An object of the present invention is to solve the above problems. Specifically, it is to prove the four-color theorem in the present application and provide a board game that can be enjoyed by competing while considering according to a unified rule using the means and the rule of the four-color theorem.

Means for Solving the Problems

[0005] In the board game of the present invention, which has a board having a map composed of a plurality of grids and a plurality of pieces having four differently colored knobs arranged according to the rule of the four-color theorem, instead of using a computer to check each case of the four-color theorem one by one, the four-color theorem is proved by means of showing the arrangement of the four colors for the entire determined region, and a board game of the four-color theorem with rules based on that means is provided.

Effects of the Invention

[0006] The board game of the present invention has the advantage of solving the four-color theorem in a way that does not use a computer, which has not been proven so far, and can provide a novel and enjoyable experience like never before.

Best Mode for Carrying Out the Invention

[0007] From here, the content of the establishment of the four-color theorem will be disclosed and explained. First, when the plane is divided centered on the center point by drawing a plurality of lines from the center point of the circle toward the circumference, when the area is divided by these plurality of lines that are boundary lines and two areas are adjacent, the interference is that the range of the line is the interference line, and the maximum number of areas where all the interference lines sharing a point interfere with each other is 3. Figures 1 to 3 show comparative examples thereof, and are schematic diagrams that simplify the areas sharing a point and an interference line and represent the combined parts. And, the vicinity of the interference line where the areas interfere with each other in a Y shape by the division by the interference line sharing a point shown in FIG. 1 is defined as Y-shaped interference, and as shown in FIG. 2, when all areas share only a point up to an infinite value, it is defined as V-shaped adjacency. Then, the division of the plane is limited to V-shaped adjacency or Y-shaped interference by three areas. However, considering the outside of the overall figure, which is the range of the designated area where the areas spread side by side, as one area, the division of the areas is similarly a Y-shaped division, but as shown in the schematic diagram of FIG. 3, this is distinguished from Y-shaped interference and defined as T-shaped interference of two areas. In the case of FIG. 5, it is replaced with FIG. 3 from the viewpoint of targeting the combined parts of the areas sharing a point and is clearly shown. Also, as shown in FIG. 6, even if we try to freely deform the extension lines of the plurality of boundary lines by regarding the circumferential part as the connection of the extension lines of the plurality of boundary lines drawn from the center point of the circle toward the circumference without changing the division method, since the extension lines of the plurality of boundary lines do not intersect each other, it is limited to two ways: either forming an area by connecting with the extension lines of the adjacent boundary lines in the order arranged in the circumferential direction without changing the connection destination, or forming an area by connecting with the boundary lines of the next area arranged in the circumferential direction so that the extension lines of the boundary lines surround several other areas in a U shape. In any case, the principle of area division in the plane has nothing to do with the shape and size of each entire area. That is, all regions in the method of partitioning a plane share some interference lines and points, and the ways of combining regions are limited to V-shaped adjacency, Y-shaped interference, and T-shaped interference where not all are regarded as interfering regions. As described above, if the region of any Y-shaped interference or T-shaped interference is a definite element, and the outside of it is an indefinite element with the number of regions and the region arrangement form, as shown in FIG. 1, the maximum number of regions where all interference lines sharing points interfere with each other is 3 + indefinite elements. By the way, as shown in FIGS. 4 and 9 when the plane is partitioned into one region, an example can be shown where the maximum number of regions that all interfere with each other is 4 by the method of including some regions within the region of the definite element. Also, FIGS. 7 and 8 are in the same form, and simply being surrounded by a plurality of regions, an example can be shown where the maximum number of regions that all interfere with each other is 4. Therefore, although it is the same thing, by surrounding a part of the indefinite element with a region so as to interfere with the region of the definite element, the indefinite element can be changed into a definite element, and it can be determined that the maximum number of regions that all interfere with each other is 4. Because these examples show all the ways where the maximum number of regions that all interfere with each other is 4, the interference with the indefinite element can be regarded as just one region in FIGS. 4 and 9, and FIG. 7 can be considered by replacing it with FIG. 1 and FIG. 8 with FIG. 9, so the combination of the number of regions that all interfere with each other is limited to a maximum of 4, and it does not become a factor to increase the maximum number of regions that all interfere with each other and the indefinite element. On the other hand, since the ways of combining regions where all interference lines sharing points interfere with each other are limited to T-shaped interference and Y-shaped interference of three regions, as shown in FIG. 10, one region within the indefinite element that Y-shaped interferes along two regions within the definite element can be newly determined and absorbed as the third region of the definite element. Similarly, as shown in FIG. 11, one region that Y-shaped interferes or V-shaped adjacents along two regions within the definite element can be successively determined as a new region of the definite element, and the regions that Y-shaped interfere and V-shaped adjacent are connected in a row like counting beads one after another, and further can be made into a belt-shaped layer as shown in FIG. 12. 14 and 17 in FIG. 12 show T-shaped interference. Therefore, as shown in Fig. 12, for the three regions of the determined elements, all the specified regions can be changed into determined elements by stacking strip-shaped region layers along the center target. Although there is also a method of expanding the regions of the determined elements radially, here it is limited to the method of creating a strip-shaped layer so that the regions are continuous and along the determined elements. The numbers in the figures from Fig. 1 to Fig. 12 up to now are those obtained by assigning different colors to the numbers. And to distribute these into four colors, since the arrangement of the four colors for the regions can be freely determined, it can be determined according to the following rules. First, to avoid the same color numbers due to region interference, since the number of colors required is 4, which is the maximum number of regions that all interfere with each other, as shown in Fig. 2, when arranging the regions so that there are two each vertically and horizontally facing each other in advance, including the case where the vertical interference line is shifted to the position of the dotted line, as shown in Fig. 13, two colors can be arranged alternately and regularly in a strip shape respectively. Next, when successively determining one region at a time as the third region of the determined elements from the undetermined elements along the two regions within the determined elements, even if three of the four colors are distributed, there is always one extra fluid color number. Therefore, as shown in Fig. 11 and Fig. 13, even when determining the number color of the one region that interferes with the three regions where different three colors are determined in advance later, the extra fluid color numbers can be arranged irregularly. Therefore, although the order of making all the regions into determined elements is not unique, as shown in Fig. 12, by arranging the regions regularly and alternately with two colors each in the circumferential direction for each strip-shaped layer centered on the target region, stacking the region layers, and determining and arranging them one by one in the order in which the regions are determined as determined elements, it is certain that the numbers from Fig. 1 to Fig. 12 can avoid the same color numbers in the interference regions and all the regions can be filled with only four numbered colors. The proof of the Four Color Theorem is that, starting from a state where any region always has at least one or more regions of different colors sandwiched between other regions of the same color, the four types of numbered-color regions can be arranged in order without interfering with regions of the same numbered color up to the entire specified region. This is the condition for the theorem to hold. For example, by assigning colors 1, 2, and 3 to the three regions 1, 2, and 3 in Figure 1 and decomposing the three regions, with any region centered on color 1 and following colors 2 and 3 as determining elements, it is sufficient to show the means of successively determining the numbered colors of the regions as shown in Figure 14 in the order of Figure 12 so that they can be arranged from color 1 to color 4. That is, it is a state where a strip-like layer of all regions of colors 2 and 3 along any region of color 1 is determined, and further a strip-like layer of regions of colors 1 and 4 along that strip-like layer is determined. The entire specified region composed of these layers overlapping alternately and repeatedly is arranged in order from color 1 to color 4. Figures 13 and 14 show that the Four Color Theorem holds no matter how the layers overlap. Therefore, it has been proven that the Four Color Theorem holds. Finally, Figure 15 shows an example where it is impossible to use a computer to check each case number of the Four Color Theorem one by one. This is because the method of using a computer attempts to assume and examine all case numbers for an infinite number of combinations of undetermined regions, starting with the fact that it requires an infinite number of interference lines, while this paper shows the means of arranging the four colors for the entire determined region. Next, the embodiments of the present invention will be described with reference to the drawings. The board game of the Four Color Theorem of the present invention is a board game having a board surface with a map composed of a plurality of squares and a plurality of pieces having four differently colored picks arranged according to the rules of the Four Color Theorem. It is a game in which the total number of pieces placed on the board surface is competed between a conquering team and a blocking team. In the first embodiment, following the rules of the four-color theorem, the game starts from any square of the attacking team, and then from any square of the defending team. The game progresses by alternately placing pieces one by one on each square for both the attacking and defending teams. The rule for placing pieces is that the attacking team can only place pieces on the squares adjacent to the square where their own team has placed a piece by an interference line, and the defending team can place pieces on the squares adjacent to the squares where the pieces of both teams have been placed by an interference line. At that time, according to the convention of the four-color theorem, it must be selected from four colors so as not to be the same color as other adjacent squares. The method of placing the pieces on the squares is to insert the opposite pick on the upper side with the effective pick color into the hole of the square. The game continues until neither team can place a piece on the board. It is a rule where the attacking and defending teams compete alternately, and the team with more pieces in the comparison of the total number of pieces on the entire board wins. Different from the four-color theorem where one can determine four colors by oneself, it is a difficult and enjoyable game to cover all squares with four colors.

Brief Explanation of the Drawings

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Claims

Claim 1 A board game characterized by having a board surface with a map composed of a plurality of squares and a plurality of pieces having four differently colored grips arranged according to the rules of the four-color theorem Claim 2 The board game according to claim 1, characterized by having holes in each of the plurality of squares and the four differently colored pieces having a structure in which one grip is inserted into this hole Claim 3 The board game according to claim 1, characterized by having two pairs of pieces having four differently colored grips configured in a cross shape of a rod

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